Blazhko RR Lyrae light curves as modulated signals

Monthly Notices of the Royal Astronomical Society (Impact Factor: 5.11). 06/2011; 417(2). DOI: 10.1111/j.1365-2966.2011.19313.x
Source: arXiv


We present an analytical formalism for the description of Blazhko RR Lyrae
light curves in which employ a treatment for the amplitude and frequency
modulations in a manner similar to the theory of electronic signal
transmitting. We assume monoperiodic RR Lyrae light curves as carrier waves and
modulate their amplitude (AM), frequency (FM), phase (PM), and as a general
case we discuss simultaneous AM and FM. The main advantages of this handling
are the following: (i) The mathematical formalism naturally explains numerous
light curve characteristics found in Blazhko RR Lyrae stars such as mean
brightness variations, complicated envelope curves, non-sinusoidal frequency
variations. (ii) Our description also explains properties of the Fourier
spectra such as apparent higher-order multiplets, amplitude distribution of the
side peaks, the appearance of the modulation frequency itself and its
harmonics. In addition, comparing to the traditional method, our light curve
solutions reduce the number of necessary parameters. This formalism can be
applied to any type of modulated light curves, not just for Blazhko RR Lyrae

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We report the discovery of amplitude and phase modulations typical of the Blazhko effect in 22 RRc and nine RRab type RR Lyrae stars in NGC 5024 (M53). This brings the confirmed Blazhko variables in this cluster to 23 RRc and 11 RRab stars, which represent 66 and 37 per cent of the total population of RRc and RRab stars in the cluster, respectively, making NGC 5024 the globular cluster with the largest presently known population of Blazhko RRc stars. We place a lower limit of 52 per cent on the overall incidence rate of the Blazhko effect among the RR Lyrae population in this cluster. New data have allowed us to refine the pulsation periods. The limitations imposed by the time span and sampling of our data prevent reliable estimations of the modulation periods. The amplitudes of the modulations range between 0.02 and 0.39 mag. The RRab and RRc are neatly separated in the colour–magnitude diagram, and the RRc Blazhko variables are on average redder than their stable counterparts; these two facts may support the hypothesis that the horizontal branch (HB) evolution in this cluster is towards the red and that the Blazhko modulations in the RRc stars are connected with the pulsation mode switch.
    Full-text · Article · Nov 2011 · Monthly Notices of the Royal Astronomical Society
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Some pulsating stars are good clocks. When they are found in binary stars, the frequencies of their luminosity variations are modulated by the Doppler effect caused by orbital motion. For each pulsation frequency this manifests itself as a multiplet separated by the orbital frequency in the Fourier transform of the light curve of the star. We derive the theoretical relations to exploit data from the Fourier transform to derive all the parameters of a binary system traditionally extracted from spectroscopic radial velocities, including the mass function which is easily derived from the amplitude ratio of the first orbital sidelobes to the central frequency for each pulsation frequency. This is a new technique that yields radial velocities from the Doppler shift of a pulsation frequency, thus eliminates the need to obtain spectra. For binary stars with pulsating components, an orbital solution can be obtained from the light curve alone. We give a complete derivation of this and demonstrate it both with artificial data, and with a case of a hierarchical eclipsing binary with {\it Kepler} mission data, KIC 4150611 (HD 181469). We show that it is possible to detect Jupiter-mass planets orbiting $\delta$ Sct and other pulsating stars with our technique. We also show how to distinguish orbital frequency multiplets from potentially similar nonradial $m$-mode multiplets and from oblique pulsation multiplets.
    Full-text · Article · Feb 2012 · Monthly Notices of the Royal Astronomical Society
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The Blazhko phenomenon, the modulation of the pulsation of RR Lyrae stars, remains one of the most stubborn unsolved problems of stellar pulsation. The recent idea of Stothers proposes that periodic variations in the properties of the convective envelope may be behind the amplitude and phase modulation. In this work, we approximated the mechanism by introducing variations in the convective parameters of the Florida–Budapest hydrodynamic code and also by means of amplitude equations. We found that the process is only effective for long modulation periods, typically for more than 100 d, in agreement with the thermal time-scales of the pulsation in RR Lyrae stars. Due to the slow response of the pulsation to the structure changes, short-period, high-amplitude Blazhko modulation cannot be reproduced with this mechanism or would require implausible variations in the convective parameters on short time-scales. We also found that the modulation of the mixing length results in strong differences between both the luminosity and radius variations and the respective phase modulations of the two quantities, suggesting notable differences between the energy output of the photosphere and the mechanical variations of the layers. The findings suggest that the convective cycle model is not well suited as a stand-alone mechanism behind the Blazhko effect.
    Preview · Article · Mar 2012 · Monthly Notices of the Royal Astronomical Society
Show more